process. It is difficult to establish that a successful network model of a social or biological process is unique in the sense that Maxwell’s equations uniquely describe the propagation of electromagnetic waves independent of the details of the associated physical environment.

The statement of task asks how a new field of investigation called network science should be defined. Given the evolving notion of a science of networks, any answer to this question will be ephemeral, and the scope and content of network science will evolve as its practitioners develop it. Proposing a formal definition entails two additional risks. First, since the various network application communities perceive this topic in different ways, some of them are likely to criticize, even reject, any definition offered. Second, in light of this possibility, differences of opinion over the definition may become a rationale for discounting the contents of this report. Nevertheless, in the spirit of providing the Army with a framework for thinking about what network science might become, the committee offers the following tentative definition:

Finding 4-3. Network science consists of the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena.

By focusing on the development of models and properties of the underlying representations, this new area of scientific investigation offers the promise of developing tools, techniques, and models that apply to multiple applications areas. It also offers the happy prospect of simplifying and codifying a variety of nomenclatures and lexicons. Thus, one may reasonably expect that creation of a field called network science will not only provide a body of rigorous results that improve the predictability of the engineering design of complex networks, but also speed up basic research in a variety of applications areas. (The defining characteristics of a network and its behaviors are explored further in Chapter 6.)

Science tells us how the world operates, and technology gives us practical applications of the resulting insights. These make their way into various sectors of society: into the medical tools, procedures, and remedies of our health-care sector, into the products and services of our economy at large, into the texts and classrooms of our educational centers, into the laws and administration of our government, and into the weapons and communications systems of our military. Paths leading to military strength, health-care excellence, a trained labor force and economic vibrancy all follow the flow from science to technology to institutional forms and applications in their plentiful variety.

These paths all have beginnings and endings, with specific tasks and characteristics at different points along the way. They begin in gestation, reach an inflection point and grow rapidly, mature when their application is readily understood and widespread, then ultimately age and decline. The quarters of a life cycle are gestation, growth, maturity, and decline. They control not only biological life, but the lives of nations and economies as well (Perez, 2002).

We see this in a seed that sprouts, flowers, and dies; in a product that passes through research and development (R&D) into the marketplace and then into every home; and in an Army that pioneers systems that spread throughout the military, then on into society at large, passing from the arcane to ubiquity and, ultimately, to obsolescence. Ultimately, all cycles are surpassed by another cycle—be it of organism, product, or weapons system—that is better adapted to the extant surroundings. In this life cycle context, network science is somewhere near the end of its gestation, poised for takeoff and growth in the decade ahead.

When new paradigms first appear, the scientific communities that pertain have little or no social organization. In the growth phase of their cycle, groups of collaborators and “invisible colleges” characteristic of a more mature science develop around their bodies of knowledge. Network science is ready to complete this first phase but is not yet ready to enter its growth stage. The Army can play a crucial role in facilitating the transition now.

Indeed, truly surprising results might arise from a systematic study of network science. For example, it is widely held that a revised military paradigm is needed to address evolving threats and opportunities associated with terrorism at home and abroad. These threats arise from network behaviors, specifically the adaptation of social networks to the increasing capabilities of communication and information networks (Arquilla and Ronfeldt, 2001; Berkowitz, 2003). This adaptive phenomenon has been observed over the centuries. Typically, engineered networks designed with one set of social behaviors in mind are, over time, exploited by disruptive elements (e.g., criminals and terrorists) for their own purposes. This is a general historical pattern, examples of which include disruption of commercial naval shipping by pirates in the 18th century, train robberies in the 19th century, airplane hijackings in the 20th century, and terrorism and cybercrime in the 21st century, including the destruction of the World Trade Center on September 11, 2001. Large infrastructure networks evolve over time; society becomes more dependent on their proper functioning; disruptive elements learn to exploit them; and society is faced with challenges, never envisaged initially, to the control and robustness of these networks. Society responds by adapting the network to the disruptive elements, but the adaptations generally are not totally satisfactory. This produces a demand for better knowledge of the design and operation of both the infrastructure networks themselves and the social networks that exploit them. This demand cannot be met by existing knowledge, because the circumstances that create it were not anticipated when the networks were designed and built.